Double Vagueness: Effect of Scale on the Modelling of Fuzzy Spatial Objects

Abstract

In the identification of landscape features vagueness arises from the fact that the attributes and parameters that make up a landscape vary over space and scale. In most existing studies, these two kinds of vagueness are studied separately. This paper investigates their combination (double vagueness) in the identification of coastal landscape units. Fuzzy set theory is used to describe the vagueness of geomorphic features based on continuity in space. The vagueness resulting from the scale of measurement is evaluated by statistical indicators. The differences of fuzzy objects derived from data at differing resolutions are studied in order to examine these higherorder uncertainties. Multi-scale analysis of the landscape is carried out using a moving window, ranging in size from 60x60 meters to 1500x1500 meters. The statistics of the fuzziness of the fuzzy landscape units are calculated, and the variability of them with scale is assessed. It shows that a major affect of scale on the mapping of geomorphic landscape units, is determination of the area of those units. This result implies that caution must be exercised in comparing landscapes at different scales and in choosing the resolution of the data that best describes the process under study.